applecare for imac bought on ebay

Nope, STRONG recommendation. NEVER EVER buy any computer from Ebay. If you want a Mac please buy directly from Apple, an Apple authorized reseller, buy an Apple refurbished unit from Apple or if you cannot afford a new or Apple refurb then contact a reputable reseller such as MacSales.com and buy from them. You have many options available to you, Ebay is about the worst option though!!!

No, unfortunately.

As to your question about being able to get Applecare for an iMac purchased on eBay the answer is it's extremely doubtful and probably not possible.